This question tests 4th grade ability to find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, properties of operations, and/or the relationship between multiplication and division (CCSS.4.NBT.6). Division separates a total into equal groups—you can think of it as sharing (divide total among groups to find size of each) or grouping (divide total into groups of certain size to find how many groups). The standard algorithm divides place by place from left to right: divide, multiply, subtract, bring down next digit, repeat. When a number doesn't divide evenly, there is a remainder (the amount left over), which must always be less than the divisor. To divide 3,276 ÷ 9, students use place value to break into parts and divide each, finding quotient 364. Choice A is correct because using the standard algorithm gives quotient 364 with no remainder, and checking with multiplication confirms: 9 × 364 = 3,276. Choice C represents stopping too early or a place value error, which happens when students forget to divide all places. To help students: Use standard algorithm steps: (1) Divide—how many times does divisor go into current dividend? (2) Multiply—quotient digit times divisor, (3) Subtract—from current dividend, (4) Bring down next digit, (5) Repeat. Connect to multiplication: what times 9 equals 3,276? Check answers with multiplication. Use place value: 3,276 ÷ 9 = (2,700 ÷ 9) + (540 ÷ 9) + (36 ÷ 9) = 300 + 60 + 4 = 364. Watch for forgetting to bring down digits or weak facts.

This question tests 4th grade ability to find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, properties of operations, and/or the relationship between multiplication and division (CCSS.4.NBT.6). Division separates a total into equal groups—you can think of it as sharing (divide total among groups to find size of each) or grouping (divide total into groups of certain size to find how many groups). The standard algorithm divides place by place from left to right: divide, multiply, subtract, bring down next digit, repeat. When a number doesn't divide evenly, there is a remainder (the amount left over), which must always be less than the divisor. To divide $945 \div 9$ into groups of 9, students use place value to break into parts and divide each, finding quotient 105 with no remainder. Choice B is correct because using multiplication: $9 \times 105 = 945$, which demonstrates understanding of division process and place value. Choice A represents a basic division fact error, which happens when students make an error in one division step. To help students: Use standard algorithm steps: (1) Divide—how many times does divisor go into current dividend? (2) Multiply—quotient digit times divisor, (3) Subtract—from current dividend, (4) Bring down next digit, (5) Repeat. For word problems with remainders, consider context—do you need another group (round up) or ignore leftovers (round down)? Check answers with multiplication: quotient × divisor + remainder should equal dividend ($105 \times 9 + 0 = 945$ ✓).

This question tests 4th grade ability to find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, properties of operations, and/or the relationship between multiplication and division (CCSS.4.NBT.6). Division separates a total into equal groups—you can think of it as sharing (divide total among groups to find size of each) or grouping (divide total into groups of certain size to find how many groups). The standard algorithm divides place by place from left to right: divide, multiply, subtract, bring down next digit, repeat. When a number doesn't divide evenly, there is a remainder (the amount left over), which must always be less than the divisor. To divide 4,096 ÷ 8, students use the standard algorithm: divide each place starting from left, finding quotient 512 with no remainder. Choice A is correct because using multiplication: 8 × 512 = 4,096, which demonstrates understanding of division process and place value. Choice B represents a basic division fact error, such as miscalculating in one step, which happens when students make an error in one division step. To help students: Use standard algorithm steps: (1) Divide—how many times does divisor go into current dividend? (2) Multiply—quotient digit times divisor, (3) Subtract—from current dividend, (4) Bring down next digit, (5) Repeat. Emphasize checking with multiplication: quotient × divisor + remainder should equal dividend (512 × 8 + 0 = 4,096 ✓), and use place value: 4,096 ÷ 8 = (3,200 ÷ 8) + (800 ÷ 8) + (96 ÷ 8) = 400 + 100 + 12 = 512.

This question tests 4th grade ability to find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, properties of operations, and/or the relationship between multiplication and division (CCSS.4.NBT.6). Division separates a total into equal groups—you can think of it as sharing (divide total among groups to find size of each) or grouping (divide total into groups of certain size to find how many groups). The standard algorithm divides place by place from left to right: divide, multiply, subtract, bring down next digit, repeat. When a number doesn't divide evenly, there is a remainder (the amount left over), which must always be less than the divisor. To solve 7 × ? = 1,176, students use the relationship to multiplication: 7 times what equals 1,176?, or divide 1,176 ÷ 7, finding quotient 168 with no remainder. Choice C is correct because using multiplication: 7 × 168 = 1,176, which demonstrates understanding of division process and place value. Choice A represents a basic division fact error, which happens when students make an error in one division step. To help students: Connect to multiplication: 1,176 ÷ 7 asks 'what times 7 equals 1,176?' Use standard algorithm steps: (1) Divide—how many times does divisor go into current dividend? (2) Multiply—quotient digit times divisor, (3) Subtract—from current dividend, (4) Bring down next digit, (5) Repeat. Check answers with multiplication: quotient × divisor + remainder should equal dividend (168 × 7 + 0 = 1,176 ✓), and watch for weak division facts preventing fluency.

This question tests 4th grade ability to find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, properties of operations, and/or the relationship between multiplication and division (CCSS.4.NBT.6). Division separates a total into equal groups—you can think of it as sharing (divide total among groups to find size of each) or grouping (divide total into groups of certain size to find how many groups). The standard algorithm divides place by place from left to right: divide, multiply, subtract, bring down next digit, repeat. When a number doesn't divide evenly, there is a remainder (the amount left over), which must always be less than the divisor. To divide 639 ÷ 5 for full bags and leftovers, students use the standard algorithm, finding quotient 127 and remainder 4. Choice B is correct because 5 × 127 = 635 with remainder 4, and checking with multiplication confirms: 5 × 127 + 4 = 639. Choice C represents a remainder ≥ divisor (invalid, since 5 ≥ 5 means divide one more time), which happens when students don't divide enough times. To help students: For word problems with remainders, consider context—full bags mean quotient, leftovers are remainder. Emphasize remainder must be less than divisor—if not, divide again. Check with multiplication: quotient × divisor + remainder = dividend (127 × 5 + 4 = 639 ✓). Use place value: 639 ÷ 5 = (500 ÷ 5) + (130 ÷ 5) + (9 ÷ 5) = 100 + 26 + 1 R4. Watch for omitting remainders or basic fact errors.

This question tests 4th grade ability to find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, properties of operations, and/or the relationship between multiplication and division (CCSS.4.NBT.6). Division separates a total into equal groups—you can think of it as sharing (divide total among groups to find size of each) or grouping (divide total into groups of certain size to find how many groups). The standard algorithm divides place by place from left to right: divide, multiply, subtract, bring down next digit, repeat. When a number doesn't divide evenly, there is a remainder (the amount left over), which must always be less than the divisor. To divide 1,509 ÷ 5, students use the standard algorithm: divide each place starting from left, finding quotient 301 with remainder 4. Choice A is correct because using multiplication: 5 × 301 + 4 = 1,505 + 4 = 1,509, which demonstrates understanding of division process and place value. Choice C represents a remainder ≥ divisor (invalid), which happens when students don't divide enough times (remainder should be less than divisor). To help students: Use standard algorithm steps: (1) Divide—how many times does divisor go into current dividend? (2) Multiply—quotient digit times divisor, (3) Subtract—from current dividend, (4) Bring down next digit, (5) Repeat. Emphasize remainder must be LESS than divisor—if remainder equals or exceeds divisor, divide one more time, and check with multiplication: quotient × divisor + remainder should equal dividend (301 × 5 + 4 = 1,509 ✓).

This question tests 4th grade ability to find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, properties of operations, and/or the relationship between multiplication and division (CCSS.4.NBT.6). Division separates a total into equal groups—you can think of it as sharing (divide total among groups to find size of each) or grouping (divide total into groups of certain size to find how many groups). The standard algorithm divides place by place from left to right: divide, multiply, subtract, bring down next digit, repeat. When a number doesn't divide evenly, there is a remainder (the amount left over), which must always be less than the divisor. To divide 672 ÷ 6, students use the standard algorithm: divide each place starting from left, finding the quotient. Choice B is correct because using the standard algorithm, 6 goes into 67 eleven times (6×11=66, subtract to get 1), bring down 2 to make 12, 6 goes into 12 two times (6×2=12, subtract to get 0), but adjusting places gives 112; checking with multiplication confirms 6×112=672. Choice A represents a basic division fact error, like miscounting in one step, which happens when students make an error in one division step. To help students: Use standard algorithm steps: (1) Divide—how many times does divisor go into current dividend? (2) Multiply—quotient digit times divisor, (3) Subtract—from current dividend, (4) Bring down next digit, (5) Repeat. Use place value: break into parts and divide each, and check answers with multiplication.

This question tests 4th grade ability to find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, properties of operations, and/or the relationship between multiplication and division (CCSS.4.NBT.6). Division separates a total into equal groups—you can think of it as sharing (divide total among groups to find size of each) or grouping (divide total into groups of certain size to find how many groups). The standard algorithm divides place by place from left to right: divide, multiply, subtract, bring down next digit, repeat. When a number doesn't divide evenly, there is a remainder (the amount left over), which must always be less than the divisor. To divide 987 ÷ 6, students use the standard algorithm: divide each place starting from left, finding quotient 164 with remainder 3. Choice A is correct because using multiplication: 6 × 164 + 3 = 984 + 3 = 987, which demonstrates understanding of division process and place value. Choice C represents omitted remainder, which happens when students forget problems can have remainders. To help students: Use standard algorithm steps: (1) Divide—how many times does divisor go into current dividend? (2) Multiply—quotient digit times divisor, (3) Subtract—from current dividend, (4) Bring down next digit, (5) Repeat. Emphasize remainder must be LESS than divisor—if remainder equals or exceeds divisor, divide one more time, and check with multiplication: quotient × divisor + remainder should equal dividend (164 × 6 + 3 = 987 ✓).

This question tests 4th grade ability to find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, properties of operations, and/or the relationship between multiplication and division (CCSS.4.NBT.6). Division separates a total into equal groups—you can think of it as sharing (divide total among groups to find size of each) or grouping (divide total into groups of certain size to find how many groups). The standard algorithm divides place by place from left to right: divide, multiply, subtract, bring down next digit, repeat. When a number doesn't divide evenly, there is a remainder (the amount left over), which must always be less than the divisor. To divide $768 \div 6$, students use the standard algorithm: 6 goes into 7 one time ($6$), subtract to get 1, bring down 6 to make 16, 6 goes into 16 two times ($12$), subtract to get 4, bring down 8 to make 48, 6 goes into 48 eight times ($48$), subtract to get 0. Choice A is correct because using the standard algorithm gives quotient 128 with no remainder, and checking with multiplication confirms: $6 \times 128 = 768$. Choice B represents a basic division fact error, such as miscalculating $48 \div 6$ as 7 instead of 8, which happens when students have weak division facts preventing fluency. To help students: Use standard algorithm steps: (1) Divide—how many times does divisor go into current dividend? (2) Multiply—quotient digit times divisor, (3) Subtract—from current dividend, (4) Bring down next digit, (5) Repeat. Emphasize checking answers with multiplication: quotient $\times$ divisor + remainder should equal dividend. Use place value: $768 \div 6 = (600 \div 6) + (120 \div 6) + (48 \div 6) = 100 + 20 + 8 = 128$. Watch for forgetting to bring down digits or errors in basic facts.

This question tests 4th grade ability to find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, properties of operations, and/or the relationship between multiplication and division (CCSS.4.NBT.6). Division separates a total into equal groups—you can think of it as sharing (divide total among groups to find size of each) or grouping (divide total into groups of certain size to find how many groups). The standard algorithm divides place by place from left to right: divide, multiply, subtract, bring down next digit, repeat. When a number doesn't divide evenly, there is a remainder (the amount left over), which must always be less than the divisor. To divide 518 ÷ 6, students use the standard algorithm: divide each place starting from left, finding quotient and remainder. Choice A is correct because using multiplication, 6×86=516, and 518-516=2, giving quotient 86 with remainder 2; this demonstrates understanding of division process and place value. Choice B represents a remainder ≥ divisor (invalid), which happens when students don't divide enough times (remainder should be less than divisor). To help students: Use standard algorithm steps: (1) Divide—how many times does divisor go into current dividend? (2) Multiply—quotient digit times divisor, (3) Subtract—from current dividend, (4) Bring down next digit, (5) Repeat. Emphasize remainder must be LESS than divisor—if remainder equals or exceeds divisor, divide one more time, and check with multiplication: quotient × divisor + remainder = dividend (86×6 +2=518 ✓).